Method for codebook enhancement for multi-user multiple-input multiple-output systems

ABSTRACT

A wireless terminal is capable of receiving a pilot signal from a base station; and determining a precoding matrix as a linear combination of two matrices V 1  and V 2  based on the received pilot signal. In one implementation, the two matrices V 1  and V 2  are sub-matrices of a matrix U of a codebook, the linear combination is u:=(V 1 +αV 2 )/√{square root over (1+|α| 2 )} and α is one of a real-valued number and a complex-valued number. The wireless terminal is also capable of transmitting a representation of at least a portion of the precoding matrix to the base station.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional PatentApplication 61/775,333, filed Mar. 8, 2013, the entirety of which isincorporated herein by reference.

TECHNICAL FIELD

The present disclosure is directed to a method and apparatus for channelfeedback in a wireless system with antenna arrays. More particularly,the present disclosure is directed to feedback from a wireless terminalto a base station.

BACKGROUND

A Multi-Input Multi-Output (“MIMO) communication system uses a pluralityof channels in a spatial area. Antenna arrays that have multipletransmission antennas can increase the capacity of data transmissionthrough MIMO transmission schemes.

Two types of MIMO transmission schemes can be employed. Single-user MIMO(SU-MIMO) involves transmitting at least one data stream to a singleuser over a time frequency resource. Multi-user MIMO (MU-MIMO) involvestransmitting at least one data stream per user to at least twoco-scheduled users over a single, i.e., same time frequency, resource.

In a MIMO communication system, base stations and mobile stations usecodebooks to enable channel state information feedback. The codebooksmay additionally be used for precoding the information streams at thetransmitter. Elements of a codebook are stored in both base stations andin mobile stations, and can be used to quantize the spatial channelstate information for feedback. Each codebook element is a vector or amatrix, depending on the dimension of the channel matrix and the numberof data streams supported. When communicating with a base station, themobile station receives a Channel State Information Reference Signal(CSI-RS) from the base station and, using the CSI-RS, determines thestate of the channel (generally referred to as Channel StateInformation(CSI)) between it and the base station and, based on thechannel state, selects a vector or a matrix from the codebook. Themobile station then “recommends” the selected vector or matrix to thebase station as part of overall CSI feedback. The base station may thenuse the recommended vector for beamforming or, more generally, therecommended matrix for precoding data streams prior to transmission viamultiple antennas. Precoding is a technique that is used to weightmultiple data streams transmitted from an antenna array in order tomaximize the throughput of the link.

Typically, MIMO systems support a maximum of eight CSI-RS ports.However, some base station antenna arrays may employ more than eightantenna elements, which exceeds the number of CSI-RS antenna portsavailable. Furthermore, large antenna arrays may require additional CSI,including precoding vector or matrix recommendations, from connectedmobile stations.

DRAWINGS

While the appended claims set forth the features of the presenttechniques with particularity, these techniques may be best understoodfrom the following detailed description taken in conjunction with theaccompanying drawings of which:

FIG. 1 is a block diagram of a system in which various embodiments maybe employed;

FIG. 2 is a block diagram of a UE according to an embodiment;

FIG. 3 is a block diagram of an eNB according to an embodiment;

FIG. 4 is a block diagram of antenna arrays at a base station accordingto possible embodiments;

FIG. 5 is an block diagram of beamforming performed by a base station inan embodiment;

FIG. 6 illustrates various embodiments of finite codebooks for quantizedfeedback of α;

FIGS. 7 and 8 depict test results according to an embodiment; and

FIG. 9 is a flowchart illustrating the operation of a wirelesscommunication device according to an embodiment.

DESCRIPTION

FIG. 1 is a block diagram of a system 100 according to an embodiment.The system 100 can include a User Equipment (UE) 110, a base stationsuch as an enhanced Node B (“eNB”) 120, a network 130, and a networkcontroller 140. The UE 110 may be a wireless terminal. For example, theUE 110 can be a wireless communication device, a wireless telephone, acellular telephone, a personal digital assistant, a pager, a personalcomputer, a selective call receiver, a tablet computer, or any otherdevice that is provided with the capability of sending and receivingcommunication signals on a network such as a wireless network. Otherpossible embodiments of the UE 110 include a camera, an automotiveproduct, a household product, a television, and a radio. Possibleembodiments of the eNB 120 include a cellular base station, an accesspoint (AP), access terminal (AT), relay node, home eNB, pico eNB, femtoeNB, Transmission Point (TP), or other device that provides accessbetween a wireless communication device and a network. The UE 110 andthe eNB 120 communicate with one another using one or more well-knowncommunication techniques, such as radio-frequency cellular signals.

The network 130 may be any type of network that is capable of sendingand receiving signals, such as wireless signals. For example, thenetwork 130 may be a wireless communication network, a cellulartelephone network, a Time Division Multiple Access (TDMA)-based network,a Code Division Multiple Access (CDMA)-based network, an OrthogonalFrequency Division Multiple Access (OFDMA)-based network, a Long TermEvolution (LTE) network, a 3rd Generation Partnership Project(3GPP)-based network, or a satellite communications network.Furthermore, the network 130 may include more than one network,including multiple types of networks. For example, the network 130 mayinclude multiple data networks, multiple telecommunications networks, ora combination of data and telecommunications networks. The networkcontroller 140 is connected to the network 130. The network controller140 may be located at a base station, at a radio network controller, oranywhere else on the network 130.

FIG. 2 is an example block diagram of the UE 110 according to anembodiment. The UE 110 can include a housing 210, a controller 220coupled to the housing 210, audio input and output circuitry 230 coupledto the housing 210, a display 240 coupled to the housing 210, atransceiver 250 coupled to the housing 210, a user interface 260 coupledto the housing 210, a memory 270 coupled to the housing 210, andmultiple antennas 280 coupled to the housing 210 and the transceiver250.

The display 240 can be a liquid crystal display (LCD), a light emittingdiode (LED) display, a plasma display, a projection display, a touchscreen, or any other device for displaying information. The transceiver250 may include a transmitter and/or a receiver. The audio input andoutput circuitry 230 can include a microphone, a speaker, a transducer,or any other audio input and output circuitry. The user interface 260can include a keypad, buttons, a touch pad, a joystick, a touch screendisplay, another additional display, or any other device useful forproviding an interface between a user and an electronic device. Thememory 270 can include a random access memory, a read only memory, anoptical memory, a subscriber identity module memory, or any other memorythat can be coupled to a wireless communication device. The UE 110 canperform the methods described in all the embodiments. The transceiver250 creates a data connection with the eNB 120 (FIG. 1). The controller210 may be any programmable processor.

FIG. 3 is a block diagram of the eNB 120 (FIG. 1), according to anembodiment. The eNB 120 includes a controller 310, a memory 320, adatabase interface 330, a transceiver 340, antenna array 345,Input/Output (I/O) device interface 350, a network interface 360, and abus 370. The eNB 120 may implement any operating system, such asMicrosoft Windows®, UNIX, or LINUX, for example.

The transceiver 340 creates a data connection with the UE 110 (FIG. 1).The controller 310 may be any programmable processor. The embodimentsdisclosed herein may also be implemented on a general-purpose or aspecial purpose computer, a programmed microprocessor or microprocessor,peripheral integrated circuit elements, an application-specificintegrated circuit or other integrated circuits, hardware/electroniclogic circuits, such as a discrete element circuit, a programmable logicdevice, such as a programmable logic array, field programmablegate-array, or the like. In general, the controller 310 may be anycontroller or processor device or devices capable of operating a basestation and implementing the disclosed embodiments.

According to a possible implementation, the memory 320 includes volatileand nonvolatile data storage. Examples include electrical, magnetic, oroptical memories, Random Access Memory (RAM), cache, and hard drives.Data may be stored in the memory 320 or in a separate database. Forexample, the database interface 330 may be used by the controller 310 toaccess the database. The database may contain any formatting data toconnect the UE 110 to the network 130.

According to a possible implementation, the I/O device interface 350 isconnected to one or more input and output devices that may include akeyboard, a mouse, a touch screen, a monitor, a microphone, avoice-recognition device, a speaker, a printer, a disk drive, or anyother device or combination of devices that accept input and/or provideoutput. The I/O device interface 350 may receive a data task orconnection criteria from a network administrator. The network interface360 may be connected to a communication device, modem, network interfacecard, a transceiver, or any other device capable of transmitting andreceiving signals to and from the network 130. The components of the eNB120 are connected via the bus 270, are linked wirelessly, or areotherwise connected.

FIG. 4 is a block diagram of the antenna array 345 (FIG. 2) according toan embodiment. In this embodiment, the antenna array 345 is a transmit(Tx) antenna grid of M×N antennas 410, and includes M dipoles and N(N>1) columns of M dipole elements arranged as N columns of M elementseach. Antennas other than dipoles may also be used. Alternatively, theantenna array 345 can include (M/2) cross-pole antenna pairs arranged asN columns of (M/2) cross-pole antenna pairs. Vertical inter-elementseparation is denoted by d_(V), where d_(V)ε{0.52,4λ} and horizontalinter-element separation is denoted by d_(V), where d_(V)ε{0.52,4λ}, andwhere λ is the wavelength applicable to the center frequency of the LTEcarrier or carrier frequency of the transmitted signal. In analternative embodiment, the antenna array 345 is a closely-spaced 4 Txantenna array having two pairs of cross-polarized antennas 430 separatedby 0.5λ. In a further embodiment, antenna array 345 is a widely-spaced 4Tx antenna array having two pairs of cross-polarized antennas 450separated by 4λ.

The eNB 120 (FIG. 1) can estimate an Angle of Departure (AoD) of a Txsignal and/or a UE 110 coarse location with respect to the antenna array345 (FIG. 2) based on an uplink Sounding Reference Signal (SRS)transmission or more generally, any uplink transmissions from the UE 110(FIG. 1), by leveraging uplink channel response reciprocity (in TimeDivision Duplex (TDD) systems) or multipath direction of arrivalreciprocity (in Frequency Division Duplex (FDD)) systems). The antennaarray 345 can be calibrated with respect to AoD, which allowsbeamsteering in the direction of the UE 110.

FIG. 5 is a block diagram that illustrates the signal processing thatthe eNB 120 (FIG. 1) carries out when communicating with the UE 110(FIG. 1) according to an embodiment. A data stream 560, which is aspatial layer that includes a sequence of modulation symbols, is firstmultiplied in multipliers 540 by complex-valued weighting factors. Theresulting baseband signals, one for each antenna 530 of the antennaarray 345 (FIG. 3) are provided to transceivers 510, which convert thebaseband signals to a carrier frequency.

The transceivers 510 may also apply filtering and additional processingto the signal. The transceiver output is then passed to power amplifiers(PA) 520, which increase the signal's power. The output of the PAs 520is then fed to the antennas 530. The phase and amplitude of the signalsin each antenna 530 can be therefore be controlled so as to obtain aconstructive signal pattern at the UE 110 (FIG. 1). The beams ortransmit radiation patterns can be adjusted in the horizontal and thevertical direction by changing the weighting factors 550.Transmission-power adjustment or deployment of beams for transmittingand receiving signals can be used to meet channel requirements.Beamforming can help to cope with multipath situations and can overcomeextra attenuation by providing extra power concentration. Beamformingcan also be used to reduce interference to adjacent cells orco-scheduled UEs within a cell or coordinating cluster of cells in caseof MU-MIMO.

The method of beamforming illustrated in FIG. 5 is only an example ofhow to implement beamforming of a data stream 560. Alternatively, theweighting factors may be applied after the signal has been translated tothe carrier frequency either immediately after the transceiver or afterthe PA or may be divided in to multiple weighting factors applied atdifferent locations in the transmit chain, e.g., a weighting factorapplied in baseband and a weighting factor applied after thetransceiver.

Precoding is a part of 3GPP Release 8 and Release 10. According to 3GPPRelease 8 and Release 10, the precoder takes as input a block of vectorsx(i)=[x⁽⁰⁾(i) . . . x^((υ-1))(i)]^(T), i=0, 1, . . . , M_(symb)^(layer)−1 from the layer mapping and generates a block of vectorsy(i)=[ . . . y^((p))(i) . . . ]^(T), i=0, 1, . . . , M_(symb) ^(ap)−1 tobe mapped onto resources on each of the antenna ports, where y^((p))(i)represents the signal for antenna port p.

Precoding for spatial multiplexing is defined by

$\begin{bmatrix}{y^{(0)}(i)} \\\vdots \\{y^{({P - 1})}(i)}\end{bmatrix} = {{W(i)}\begin{bmatrix}{x^{(0)}(i)} \\\vdots \\{x^{({\upsilon - 1})}(i)}\end{bmatrix}}$

where the precoding matrix W(i) is of size P×υ and i=0, 1, . . . ,M_(symb) ^(ap)−1, M_(symb) ^(ap)=M_(symb) ^(layer).

For spatial multiplexing, the values of W(i) can be selected among theprecoder elements in the codebook configured in the eNodeB and the UE.The eNodeB can further confine the precoder selection in the UE to asubset of the elements in the codebook using codebook subsetrestrictions.

Release 8 precoding for two antenna ports (2 Tx) and four antenna ports(4 Tx) can be of the form as below.

For transmission on two antenna ports, pε{0,1}, the precoding matrixW(i) can be selected from Table 1 or a subset thereof. For theclosed-loop spatial multiplexing transmission mode, the codebook index 0is not used when the number layers is υ=2.

TABLE 1 Codebook for transmission on antenna ports {0, 1} CodebookNumber of layers v index 1 2 0 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ 1 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}$ 3 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}$ —

For transmission on four antenna ports, pε{0,1,2,3}, the precodingmatrix W can be selected from Table 2 or a subset thereof. The quantityW_(n) ^({s}) denotes the matrix defined by the columns given by the set{s} from the expression W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n) where Iis the 4×4 identity matrix and the vector u_(n) is given by Table 2.

TABLE 2 Codebook for transmission on antenna ports{0, 1, 2, 3} CodebookNumber of layers υ index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀ ^({1})W₀ ^({14})/{square root over (2)} W₀ ^({124})/{square root over (3)} W₀^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁ ^({12})/{square root over(2)} W₁ ^({123})/{square root over (3)} W₁ ^({1234})/2 2 u₂ = [1 1 −11]^(T) W₂ ^({1}) W₂ ^({12})/{square root over (2)} W₂ ^({123})/{squareroot over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1 −j]^(T) W₃ ^({1}) W₃^({12})/{square root over (2)} W₃ ^({123})/{square root over (3)} W₃^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)} −j (1 − j){squareroot over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square root over (2)} W₄^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1 − j)/{squareroot over (2)} j (−1 − j){square root over (2)}]^(T) W₅ ^({1}) W₅^({14})/{square root over (2)} W₅ ^({124})/{square root over (3)} W₅^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{squareroot over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over (2)} W₆^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

In Release 10 precoding for eight Tx antenna ports, each PrecodingMatrix Indicator (PMI) value corresponds to a pair of codebook indicesgiven in Table 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, or 3-8, where thequantities φ_(n) and v_(m) are given by

φn=e ^(jπn/2)

v _(m)=[1e ^(j2πm/32) e ^(j4πm/32) e ^(j6πm/32)]^(T)

as follows: For 8 antenna ports {15,16,17,18,19,20,21,22}, a first PMIvalue of n₁ε{0,1, . . . , f(υ)−1} and a second PMI value of n₂ε{0,1, . .. , g(υ)−1}corresponds to the codebook indices n₁ and n₂ given in Table3-j with υ equal to the associated rank indication (RI) value and wherej=υ, f(υ)={16,16,4,4,4,4,4,1} and g(υ)={16,16,16,8,1,1,1,1}.

TABLE 3-1 Codebook for 1-layer CSI reporting using antenna ports 15 to22. i₂ i₁ 0 1 2 3 0-15 W_(2i) ₁ _(,0) ⁽¹⁾ W_(2i) ₁ _(,1) ⁽¹⁾ W_(2i) ₁_(,2) ⁽¹⁾ W_(2i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(2i) ₁ _(+1,0) ⁽¹⁾W_(2i) ₁ _(+1,1) ⁽¹⁾ W_(2i) ₁ _(+1,2) ⁽¹⁾ W_(2i) ₁ _(+1,3) ⁽¹⁾ i₂ i₁ 8 910 11 0-15 W_(2i) ₁ _(+2,0) ⁽¹⁾ W_(2i) ₁ _(+2,1) ⁽¹⁾ W_(2i) ₁ _(+2,2)⁽¹⁾ W_(2i) ₁ _(+2,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(2i) ₁ _(+3,0) ⁽¹⁾W_(2i) ₁ _(+3,1) ⁽¹⁾ W_(2i) ₁ _(+3,2) ⁽¹⁾ W_(2i) ₁ _(+3,3) ⁽¹⁾${{where}\mspace{14mu} W_{m,n}^{(1)}} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} \\{\phi_{n}v_{m}}\end{bmatrix}}$

TABLE 3-2 Codebook for 2-layer CSI reporting using antenna ports 15 to22. i₂ i₁ 0 1 2 3 0-15 W_(2i) ₁ _(,2i) ₁ _(,0) ⁽²⁾ W_(2i) ₁ _(,2i) ₁_(,1) ⁽²⁾ W_(2i) ₁ _(+1,2i) ₁ _(+1,0) ⁽²⁾ W_(2i) ₁ _(+1,2i) ₁ _(+1,1)⁽²⁾ i₂ i₁ 4 5 6 7 0-15 W_(2i) ₁ _(+2,2i) ₁ _(+2,0) ⁽²⁾ W_(2i) ₁ _(+2,2i)₁ _(+2,1) ⁽²⁾ W_(2i) ₁ _(+3,2i) ₁ _(+1,0) ⁽²⁾ W_(2i) ₁ _(+3,2i) ₁_(+1,1) ⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(2i) ₁ _(,2i) ₁ _(+1,0) ⁽²⁾ W_(2i) ₁_(,2i) ₁ _(+1,1) ⁽²⁾ W_(2i) ₁ _(+1,2i) ₁ _(+2,0) ⁽²⁾ W_(2i) ₁ _(+1,2i) ₁_(+2,1) ⁽²⁾ i₁ i₂ 12 13 14 15 0-15 W_(2i) ₁ _(,2i) ₁ _(+3,0) ⁽²⁾ W_(2i)₁ _(,2i) ₁ _(+3,1) ⁽²⁾ W_(2i) ₁ _(+1,2i) ₁ _(+3,0) ⁽²⁾ W_(2i) ₁ _(+1,2i)₁ _(+3,1) ⁽²⁾${{where}\mspace{14mu} W_{m,n}^{(1)}} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} \\{\phi_{n}v_{m}}\end{bmatrix}}$

TABLE 3-3 Codebook for 3-layer CSI reporting using antenna ports 15 to22. i₂ i₁ 0 1 2 0-3 W_(8i) ₁ _(,8i) ₁ _(,8i) ₁ ₊₈ ⁽³⁾ W_(8i) ₁ _(+8,8i)₁ _(,8i) ₁ ₊₈ ⁽³⁾ {tilde over (W)}_(8i) ₁ _(,8i) ₁ _(+8,8i) ₁ ₊₈ ⁽³⁾ i₂i₁ 3 4 5 0-3 {tilde over (W)}_(8i) ₁ _(+8,8i) ₁ _(,8i) ₁ ⁽³⁾ W_(8i) ₁_(+2,8i) ₁ _(+2,8i) ₁ ₊₁₀ ⁽³⁾ W_(8i) ₁ _(+10,8i) ₁ _(+2,8i) ₁ ₊₁₀ ⁽³⁾ i₂i₁ 6 7 8 0-3 {tilde over (W)}_(8i) ₁ _(+2,8i) ₁ _(+10,8i) ₁ ₊₁₀ ⁽³⁾{tilde over (W)}_(8i) ₁ _(+10,8i) ₁ _(+2,8i) ₁ ₊₂ ⁽³⁾ W_(8i) ₁ _(+4,8i)₁ _(+4,8i) ₁ ₊₁₂ ⁽³⁾ i₂ i₁ 9 10 11 0-3 W_(8i) ₁ _(+12,8i) ₁ _(+4,8i) ₁₊₁₂ ⁽³⁾ {tilde over (W)}_(8i) ₁ _(+4,8i) ₁ _(+12,8i) ₁ ₊₁₂ ⁽³⁾ {tildeover (W)}_(8i) ₁ _(+12,8i) ₁ _(+4,8i) ₁ ₊₄ ⁽³⁾ i₂ i₁ 12 13 14 0-3 W_(8i)₁ _(+6,8i) ₁ _(+6,8i) ₁ ₊₁₄ ⁽³⁾ W_(8i) ₁ _(+14,8i) ₁ _(+6,8i) ₁ ₊₁₄ ⁽³⁾{tilde over (W)}_(8i) ₁ _(+6,8i) ₁ _(+14,8i) ₁ ₊₁₄ ⁽³⁾ i₂ i₁ 15 0-3{tilde over (W)}_(8i) ₁ _(+14,8i) ₁ _(+6,8i) ₁ ₊₆ ⁽³⁾${{{{where}\mspace{14mu} W_{m,m^{\prime},m^{''}}^{(3)}} = {\frac{1}{\sqrt{24}}\begin{bmatrix}v_{m} & v_{m^{\prime}} & v_{m^{''}} \\v_{m} & {- v_{m^{\prime}}} & {- v_{m^{''}}}\end{bmatrix}}},}\;$${\overset{\sim}{W}}_{m,m^{\prime},m^{''}}^{(3)} = {\frac{1}{\sqrt{24}}\begin{bmatrix}v_{m} & v_{m^{\prime}} & v_{m^{''}} \\v_{m} & v_{m^{\prime}} & {- v_{m^{''}}}\end{bmatrix}}$

TABLE 3-4 Codebook for 4-layer CSI reporting using antenna ports 15 to22. i₂ i₁ 0 1 2 3 0-3 W_(8i) ₁ _(,8i) ₁ _(+8,0) ⁽⁴⁾ W_(8i) ₁ _(,8i) ₁_(+8,1) ⁽⁴⁾ W_(8i) ₁ _(+2,8i) ₁ _(+10,0) ⁽⁴⁾ W_(8i) ₁ _(+2,8i) ₁_(+10,1) ⁽⁴⁾ i₂ i₁ 4 5 6 7 0-3 W_(8i) ₁ _(+4,8i) ₁ _(+12,0) ⁽⁴⁾ W_(8i) ₁_(+4,8i) ₁ _(+12,1) ⁽⁴⁾ W_(8i) ₁ _(+6,8i) ₁ _(+14,0) ⁽⁴⁾ W_(8i) ₁_(+6,8i) ₁ _(+14,1) ⁽⁴⁾${{where}\mspace{14mu} W_{m,m^{\prime},n}^{(4)}} = {\frac{1}{\sqrt{32}}\begin{bmatrix}v_{m} & v_{m^{\prime}} & v_{m} & v_{m^{\prime}} \\{\phi_{n}v_{m}} & {\phi_{n}v_{m^{\prime}}} & {{- \phi_{n}}v_{m}} & {{- \phi_{n}}v_{m^{\prime}}}\end{bmatrix}}$

TABLE 3-5 Codebook for 5-layer CSI reporting using antenna ports 15 to22. i₂ i₁ 0 0-3 $W_{i_{1}}^{(5)} = {\frac{1}{\sqrt{40}}\begin{bmatrix}v_{2i_{1}} & v_{2i_{1}} & v_{{2i_{1}} + 8} & v_{{2i_{1}} + 8} & v_{{2i_{1}} + 16} \\v_{2i_{1}} & {- v_{2i_{1}}} & v_{{2i_{1}} + 8} & {- v_{{2i_{1}} + 8}} & v_{{2i_{1}} + 16}\end{bmatrix}}$

TABLE 3-6 Codebook for 6-layer CSI reporting using antenna ports 15 to22. i₂ i₁ 0 0-3 $W_{i_{1}}^{(6)} = {\frac{1}{\sqrt{48}}\begin{bmatrix}v_{2i_{1}} & v_{2i_{1}} & v_{{2i_{1}} + 8} & v_{{2i_{1}} + 8} & v_{{2i_{1}} + 16} & v_{{2i_{1}} + 16} \\v_{2i_{1}} & {- v_{2i_{1}}} & v_{{2i_{1}} + 8} & {- v_{{2i_{1}} + 8}} & v_{{2i_{1}} + 16} & {- v_{{2i_{1}} + 16}}\end{bmatrix}}$

TABLE 3-7 Codebook for 7-layer CSI reporting using antenna ports 15 to22. i₂ i₁ 0 0-3 $\begin{matrix}{W_{i_{1}}^{(7)} =} \\{\frac{1}{\sqrt{56}}\begin{bmatrix}v_{2i_{1}} & v_{2i_{1}} & v_{{2i_{1}} + 8} & v_{{2i_{1}} + 8} & v_{{2i_{1}} + 16} & v_{{2i_{1}} + 16} & v_{{2i_{1}} + 24} \\v_{2i_{1}} & {- v_{2i_{1}}} & v_{{2i_{1}} + 8} & {- v_{{2i_{1}} + 8}} & v_{{2i_{1}} + 16} & {- v_{{2i_{1}} + 16}} & v_{{2i_{1}} + 24}\end{bmatrix}}\end{matrix}\quad$

TABLE 3-8 Codebook for 8-layer CSI reporting using antenna ports 15 to22. i₂ i₁ 0 0 $\begin{matrix}{W_{i_{1}}^{(8)} =} \\{\frac{1}{8}\begin{bmatrix}v_{2i_{1}} & v_{2i_{1}} & v_{{2i_{1}} + 8} & v_{{2i_{1}} + 8} & v_{{2i_{1}} + 16} & v_{{2i_{1}} + 16} & v_{{2i_{1}} + 24} & v_{{2i_{1}} + 24} \\v_{2i_{1}} & {- v_{2i_{1}}} & v_{{2i_{1}} + 8} & {- v_{{2i_{1}} + 8}} & v_{{2i_{1}} + 16} & {- v_{{2i_{1}} + 16}} & v_{{2i_{1}} + 24} & {- v_{{2i_{1}} + 24}}\end{bmatrix}}\end{matrix}\quad$

For a Release 10, 8 Tx codebook, precoding can be represented as

y=W ₁ W ₂ x  (Equation 1)

where W₁ can be a wideband precoder that takes advantage of thecorrelation properties of the channel, properties which are long-term innature, and W₂ performs co-phasing on a short-term basis. Here, x is thevector of modulated symbols and y is the vector of signal transmittedfrom each PA. The matrix W₁ has the structure

$\begin{matrix}{W_{1} = \begin{bmatrix}\overset{\sim}{W} & 0 \\0 & \overset{\sim}{W}\end{bmatrix}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

where the N_(T)/2×r matrix {tilde over (W)} has columns taken from anoversampled Discrete Fourier Transform (DFT) matrix. The 2r×r co-phasingmatrix W₂ is of the form

$\begin{matrix}{{W_{2} = \begin{bmatrix}1 \\\alpha\end{bmatrix}};{\alpha \in \left\{ {1,{- 1},j,{- j}} \right\}}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

for rank 1 and

$\begin{matrix}{{W_{2} = \begin{bmatrix}1 & 0 \\0 & 1 \\\alpha & 0 \\0 & {- \alpha}\end{bmatrix}};{\alpha \in \left\{ {1,j} \right\}}} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$

for rank 2.

The present disclosure sets forth 4 Tx codebook enhancements that may beused as further enhancements to the DL-MIMO Work Item in LTE Release 12in an embodiment. It has been proposed that the existing codebooks(Release 8) based on Householder reflections are sufficient. It has alsobeen proposed that there is a need to define\a dual codebook structure(similar to the Release 10 8-Tx codebook in principle). The Householderreflections-based 4 Tx codebook is not ideally suited for MU-MIMOscheduling as the limited 4-bit PMI feedback results in suboptimalBlock-Zero Forcing (ZF) or Zero-Forcing Dirty Paper Coding (ZF-DPC)implementations at the eNB. This leads to co-scheduled user interferenceat the receiver limiting the sum rate.

To illustrate, consider a K-user system with each user equipped Nreceive antennas and the base station equipped with M (<K) Tx antennas.For simplicity, consider the case of N=1 receive antennas at each user.The received signal vector at the K users can be written as

y=HUs+v

where H is the K×M channel matrix, U is the M×M precoding matrix, s isthe M×1 Tx signal vector and the co-channel interference plus noise, n,is complex Gaussian, i.e., v˜CN(0,σ² I). The sum-rate for this system is

${R(U)}:={\sum\limits_{m = 1}^{M}\; {\log_{2}\left( {1 + \frac{M^{- 1}{{h_{k{(m)}}^{*}u_{k{(m)}}}}^{2}}{\sigma^{2} + {M^{- 1}{\sum\limits_{l \neq {k{(m)}}}^{\;}\; {{h_{l}^{*}u_{l}}}^{2}}}}} \right)}}$

where h*_(k) is the k-th row of H, u_(k) is the k-th column of U andk(m) denotes the user selected for the m-th stream. In the large-SNRregime (σ²→0), the ergodic sum-rate can be written as

${{E\left\lbrack {R(U)} \right\rbrack}\overset{\sigma^{2}\rightarrow 0}{\rightarrow}{E\left\lbrack {\sum\limits_{m = 1}^{M}\; {\log_{2}\left( {1 + \frac{{{h_{k{(m)}}^{*}u_{k{(m)}}}}^{2}}{\sum\limits_{l \neq {k{(m)}}}^{\;}\; {{h_{k{(m)}}^{*}u_{l}}}^{2}}} \right)}} \right\rbrack}} = {{E\left\lbrack {\sum\limits_{m = 1}^{M}\; {\log_{2}\left( {1 + \frac{{{h_{k{(m)}}^{*}u_{k{(m)}}}}^{2}}{{h_{k{(m)}}^{*}}^{2} - {{h_{k{(m)}}^{*}u_{k{(m)}}}}^{2}}} \right)}} \right\rbrack} = {{E\left\lbrack {\sum\limits_{m = 1}^{M}\; {\log_{2}\left( {1 + \frac{{h_{k{(m)}}^{*}}^{2}}{{h_{k{(m)}}^{*}}^{2} - {{h_{k{(m)}}^{*}u_{k{(m)}}}}^{2}}} \right)}} \right\rbrack} = {- {E\left\lbrack {\sum\limits_{m = 1}^{M}\; {\log_{2}\left( {1 - {{g_{k{(m)}}^{*}u_{k{(m)}}}}^{2}} \right)}} \right\rbrack}}}}$

under the assumption that U is unitary andg*_(k(m)):=h*_(k(m))/|h*_(k(m))|.

If the UEs use a first codebook that allows the eNB to realize a certainset of absolute values of the inner products {|g*_(k(m))u_(k(m))|C₁} andthere exists a second codebook that allows the eNB to realize a secondset of inner products {|g*_(k(m))u_(k(m))|C₂} such that

g_(k(m))^(*)u_(k(m))_(C₂) > g_(k(m))^(*)u_(k(m))_(C₁)

holds with non-zero probability, then the MU-MIMO sum rate can beincreased.

In an embodiment, codebook enhancement by linear extension can be usedto increase the MU-MIMO sum rate. Suppose that the B-bit rank-L codebookcomprising M×L matrices is denoted as C^((L))={U_(j):1≦j≦2^(B)} wherethe columns within each matrix are mutually orthonormal. If v₁ and v₂are two distinct columns of some UεC^((L)), the vector formed by thelinear extension u:=(v₁+αv₂)/√{square root over (1+|α|²)} is also a unitvector, where a is a real or complex-valued number.

A Release 8, 4 Tx codebook has the property that the unit vectorscomprising the C⁽¹⁾ codebook are one of the 4 columns of a correspondingmatrix in the C⁽⁴⁾ codebook. Therefore, the codebook enhancement can beviewed as a 2-step process:

-   -   1. The k-th UE can be configured to feed back the best v₁ vector        using rank-1 feedback (e.g., using an appropriate codebook        subset restriction).    -   2. Since v₁ is a column of some matrix UεC⁽⁴⁾, the UE can then        find a v₂ (different from v₁) which is another distinct column        from U so as to maximize the inner product |h*_(k)u| where:

u:=(v ₁ +αv ₂)/√{square root over (1+|α|²)}  (Equation 5)

-   -   a. In an embodiment, only ┌log₂ M┐=2 (M=4) additional bits are        required to feedback        -   i. the index of v₂ given that v₁ has been selected by the            usual rank-1 PMI feedback and        -   ii. the case when α=0 (or v₂=0) is optimal    -   b. The parameter α can be fixed (in the specification) or can be        quantized to a B′ bit codebook and fed back to the base station.

Multiple-Input Single-Output (MISO) Receiver SNR with Codebook LinearExtension.

For simplicity, α can be real valued. A MISO receiver at the UE selectsa PMI vector so as to maximize the inner product |g*_(k)u|, whereg_(k)=h_(k)/|h_(k)|. Note that

${{g_{k}^{*}u}}^{2} = {\frac{1}{1 + \alpha^{2}}{\left( {{{g_{k}^{*}v_{1}}}^{2} + {\alpha^{2}{{g_{k}^{*}v_{2}}}^{2}} + {2\; \alpha \; {{Re}\left( {g_{k}^{*}v_{1}v_{2}^{*}g_{k}} \right)}}} \right).}}$

Futhermore,

a ₂ :=|g* _(k) v ₁|²

b ₂ :=|g* _(k) v ₂|²

c:=Re(g* _(k) v ₁ v* ₂ g _(k))/ab

In an embodiment, 0≦|c|≦1 and b²≦a², the latter by the virtue of thefact

${\alpha^{2} = {\frac{1}{z} - 1}},$

that rank-1 PMI feedback selected v₁. By change of variablesf(z):=|g*_(k)u|²=a² z+b²(1−z)±2abc√{square root over (z−z²)} is derived.The sign ambiguity comes from a choice for the change of variables. Itis also possible that ½<z≦1 and

${f^{\prime}(z)} = {a^{2} - {b^{2} \pm \frac{c\left( {1 - {2\; z}} \right)}{\sqrt{z - z^{2}}}}}$${f^{''}(z)} = {\pm \frac{- c}{2\left( {z - z^{2}} \right)^{\frac{3}{2}}}}$

By selecting a positive solution for α (for a given v₂, a positivesolution is used for α (i.e., α>0) when c>0; otherwise choose a negativesolution for α), it can be ensured that f(z) is concave and has a uniquemaximum.

It can be noted that

f(z)−a ²=√{square root over (1−z)}{−(a ² −b ²)√{square root over(1−z)}±2abc√{square root over (z)}}.

If a=b, i.e., |g*_(k)v₁|=|g*_(k) v₂|, selecting the positive root for α(again, for a given v₂, a positive solution is used for α (i.e., α>0)when c>0; otherwise choose a negative solution for α) leads to f(z)−a²>0or |g*_(k)u|>|g*_(k)v₁|.

For a>b, by selecting

$\frac{1}{\alpha^{2}} = {\frac{z}{1 - z} > \frac{\left( {a^{2} - b^{2}} \right)^{2}}{4\; c^{2}a^{2}b^{2}}}$

it is determined that f(z)−a²>0 or |g*_(k)u|>|g*_(k)v₁|.

As understood from the foregoing, the maximum absolute value of innerproduct |g*_(k)u| can be increased by allowing linear extensions to thecodebook leading to an improvement in the supported SNR and the reportedCQI.

UE Feedback

In an embodiment, a UE can select a best v₁, v₂ and α jointly such that

$\left( {v_{1},v_{2},\alpha} \right) = {\arg \; {\max\limits_{({v_{1},v_{2},\alpha})}{{g_{k}^{*}u}}^{2}}}$

The range zε(0.5,1] can be sampled (e.g., uniformly sampled) with B′bits and the corresponding α can be fed back to the base station alongwith a 2-bit feedback for v₂. Alternatively, α can be directly quantizedwith B′ bits and the corresponding α can be fed back to the base stationalong with a 2-bit feedback for v₂. With this approach, the PMI feedbackcomprises

1. 4-bit PMI to feedback v₁

2. 2-bit PMI to feedback v₂

3. B′ bits to feedback α.

α, v₂ and/or v₁ may be fed back separately (separate encoding e.g.mapped to different set of bits in a message) or two or more of α, v₂and v₁ may be jointly encoded and fed back by the UE in one CSI (ChannelState Information) report. For example, v₁ may be fed back as donecurrently in Releases 8-11 using a 4-bit PMI indicator and (α, v₂) maybe jointly encoded and fed-back as a X-bit indicator.

The PMI feedback of v₁, α, v₂ may be in the same uplink subframe or indifferent uplink subframes. The uplink subframe carrying PMI feedback ofv₁, α, and/or v₂, may also carry other CSI related information such asRank Indicator (RI), Precoding Type Indicator (PTI), and CQI (ChannelQuality Information) conditioned on the selected PMI u. The CQI may bewideband CQI (e.g., spanning the entire downlink system bandwidth) orsubband CQI (e.g., a set of k contiguous PRBs (Physical Resource Blocks)where k is a function of system bandwidth). For example, the 4-bit PMIindicator for v₁ may be indicated in a first subframe and the α, v₂ maybe indicated in a second uplink subframe, the second uplink subframebeing different than the first uplink subframe. The first uplinksubframe may carry other CSI related information such as a RankIndicator (RI). The second uplink subframe may carry other CSI relatedinformation such as a CQI. In another embodiment, the RI and the PTI maybe indicated in a CSI report in a subframe other than the first andsecond subframe.

In a second approach, a is fixed (in the specification) and UE selectsbest v₁ and v₂ such that

$\left( {v_{1},v_{2}} \right) = {\arg {\max\limits_{({v_{1},v_{2}})}{{{g_{k}^{*}u}}^{2}.}}}$

With this approach, the components of PMI are same as described aboveexcept that feedback for α is absent.

For case of α being fixed, v₂ can be fed back using a 2-bit PMI (secondPMI) indicator (including a state for the case of v₂=0 or α=0). The PMIfeedback of v₁, v₂ may be in the same uplink subframe or in differentuplink subframes. For example, the 4-bit PMI indicator for v₁ may beindicated in a first subframe and the 2-bit PMI indicator v₂ may beindicated in a second uplink subframe, the second uplink subframe beingdifferent than the first uplink subframe. The uplink subframe carryingPMI feedback of v₁ and/or v₂, may also carry other CSI relatedinformation such as Rank Indicator (RI), Precoding Type Indicator (PTI),and CQI (Channel Quality Information) conditioned on the selected PMI u.The CQI may be wideband CQI (e.g., spanning the entire downlink systembandwidth) or subband CQI (e.g., a set of k contiguous PRBs (PhysicalResource Blocks) where k is a function of system bandwidth).

For example, the 4-bit PMI indicator for v₁ may be indicated in a firstsubframe and the v₂ may be indicated in a second uplink subframe, thesecond uplink subframe being different than the first uplink subframe.The first uplink subframe may carry other CSI related information suchas a Rank Indicator (RI). The second uplink subframe may carry other CSIrelated information such as a CQI. In another embodiment, the RI and thePTI may be indicated in a CSI report in a subframe other than the firstand second subframe.

Relation of Linear Extension to W₁ W₂ Product Form

The overall precoding matrix can be written down in product form asbelow.

$P = {\underset{\underset{W_{1}}{}}{\left\lbrack {{U\left( {:{,1}} \right)}\mspace{14mu} {U\left( {:{,2}} \right)}\mspace{14mu} {U\left( {:{,3}} \right)}\mspace{14mu} {U\left( {:{,4}} \right)}} \right\rbrack}\underset{\underset{W_{2}}{}}{\begin{bmatrix}{1/\sqrt{1 + {\alpha }^{2}}} \\{\alpha_{2}/\sqrt{1 + {\alpha }^{2}}} \\{\alpha_{3}/\sqrt{1 + {\alpha }^{2}}} \\{\alpha_{4}/\sqrt{1 + {\alpha }^{2}}}\end{bmatrix}}}$

where only one of α₂, α₃ and α₄ is equal to α and the remainder arezeros and where UεC⁽⁴⁾.

Linear Extension for Rank>1

This approach can be extended to the multiple rank (rank>1) case byadding more columns to the second matrix in the product form.Specifically, for rank 2:

$P = {\underset{\underset{W_{1}}{}}{\left\lbrack {{U\left( {:{,1}} \right)}\mspace{14mu} {U\left( {:{,2}} \right)}\mspace{14mu} {U\left( {:{,3}} \right)}\mspace{14mu} {U\left( {:{,4}} \right)}} \right\rbrack}\underset{\underset{W_{2}}{}}{c_{norm}\begin{bmatrix}1 & \alpha_{12} \\\alpha_{21} & \alpha_{22} \\\alpha_{31} & \alpha_{32} \\\alpha_{41} & \alpha_{42}\end{bmatrix}}}$${{where}\mspace{14mu} c_{norm}} = \left( {1 + {\alpha_{12}}^{2} + {\sum\limits_{i = 2}^{4}\; {\sum\limits_{j = 1}^{2}\; {\alpha_{ij}}^{2}}}} \right)^{{- 1}/2}$${{{{and}\mspace{14mu} \alpha_{12}} + {\sum\limits_{i = 2}^{4}\; {\alpha_{i\; 1}{\overset{\_}{\alpha}}_{j\; 2}}}} = 0},$

thus ensuring that the precoder has unit power and the columns of theoverall precoder are orthogonal.

In LTE Release 8, for rank 2, α₁₂=0, α₂₁=α₃₁=α₄₁=0 and α₁₂=1 for onlyone i>1. For the rank 2 precoding matrices for which α₂₂=1, linearextension to the rank 2 codebook can be formed by letting the secondmatrix take one the following two alternative forms:

${W_{2} = {{{c_{norm}\begin{bmatrix}1 & 0 \\0 & 1 \\\alpha_{31} & 0 \\0 & \alpha_{42}\end{bmatrix}}\mspace{14mu} {and}\mspace{14mu} W_{2}} = {c_{norm}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & \alpha_{32} \\\alpha_{41} & 0\end{bmatrix}}}}\mspace{11mu},$

where the α_(ij)'s shown are non-zero. Extending the Release 8 codebookfor rank 3 and rank 4 needs further consideration.

General Representation in Product Form

Linear extension can be represented in a general form:

$P = {\underset{\underset{W_{1}}{}}{\left\lbrack {{U\left( {:{,1}} \right)}\mspace{14mu} {U\left( {:{,2}} \right)}\mspace{14mu} \ldots \mspace{14mu} {U\left( {:{,n}} \right)}} \right\rbrack}\underset{\underset{W_{2}}{}}{c_{norm}\begin{bmatrix}\alpha_{1,1} & \ldots & \alpha_{1,v} \\\vdots & \ddots & \vdots \\\alpha_{n,1} & \ldots & \alpha_{n,v}\end{bmatrix}}}$

where U is a N_(TX)×n matrix from a codebook with unit-norm columns, U(:, j) is the j-th columns of U, α_(j,k) are real-valued orcomplex-valued numbers, and v is the number of spatial layers or rankassociated with the precoding matrix P.

Since,

$P = {c_{norm}\left\lbrack {{\sum\limits_{j = 1}^{n}\; {\alpha_{j,1}{U\left( {:{,j}} \right)}}},{\sum\limits_{j = 1}^{n}\; {\alpha_{j,2}{U\left( {:{,j}} \right)}\mspace{14mu} \ldots \mspace{14mu} {\sum\limits_{j = 1}^{n}\; {\alpha_{j,v}{U\left( {:{,j}} \right)}}}}}} \right\rbrack}$

the k-th column of P (k=1, . . . , ν) is a linear combination ofdistinct columns of U.

Rank-1 Codebook

In an embodiment, the set of precoders are denoted by a set of 64vectors v_(i), iε{0, 1, . . . , 63}, each of length 4. The first 16precoders of the codebook are given by the 16 Release 8 precodingmatrices,) V_(i)=W_(i) ⁽¹⁾, i={0, 1, . . . , 15},

where W_(i) ⁽¹⁾, i={0, 1, . . . , 15} are defined in Table 2. W_(n)^((s)) denotes the matrix defined by the column set (s) of the unitarymatrix W_(n) formed by Householder reflections, whereW_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n) where I is the 4×4 identitymatrix and the vector u_(n) is given by Table 2.

The remaining 48 precoders are the set of all possible precoders of theform:

$v_{k} = \frac{W_{i{(k)}}^{(1)} + {\alpha \; W_{i{(k)}}^{(j)}}}{\left( {1 + {\alpha }^{2}} \right)^{1/2}}$

where j≠1, j={2, 3, 4}. We can choose a fixed value for α (e.g., a equalto 0.8).

In an embodiment, the UE can first choose the best Release 8 precoderwithin the existing set of 16 rank-1 precoders v_(i)=W_(i) ⁽¹⁾={0, 1, .. . , 15}, and then can determine if this best Release 8 precoder (withcodebook index i) can be improved by linear combination with any one ofthe column vectors (scaled by α) W_(i) ⁽²⁾, W_(i) ⁽³⁾, and W_(i) ⁽⁴⁾.With this codebook structure, the UE processing can be simplified intotwo steps:

Step 1. UE selects the best W_(i) ⁽¹⁾ from a set of 16 candidates

Step 2. UE selects the best W_(i) ^((j)) from the set of {0, W_(i) ⁽²⁾,W_(i) ⁽³⁾, W_(i) ⁽⁴⁾} where 0 is the null vector conditioned on alreadyselected best W_(i) ⁽¹⁾ from Step 1.

Accordingly, the UE is able to select the pair (W_(i) ⁽¹⁾, W_(i) ^((j)))based on evaluating an SINR (or CQI) metric over a total of 19candidates (as opposed to 16 candidates in Release 8 for rank-1feedback). The last three candidates are linear combinations of Release8 rank-1 precoding vectors that depend on the selected W_(i) ⁽¹⁾.

The four candidates in Step 1 and Step 2 above can be written as:

$v_{k} = {{\underset{\underset{W_{1}}{}}{\left\lbrack {W_{i}^{(1)},W_{i}^{(2)},W_{i}^{(3)},W_{i}^{(4)}} \right\rbrack}\underset{\underset{W_{2}}{}}{\frac{1}{\left( {1 + {\alpha }^{2}} \right)^{1/2}}\begin{bmatrix}1 \\a_{2} \\a_{3} \\a_{4}\end{bmatrix}}} = {W_{1}W_{2}}}$

where only one α_(j)=α for exactly one value of j such that 2≦j≦4 andequal to zero otherwise. The precoding vector v_(k) complies with theW₁W₂ product form where W₁ can correspond to wideband PMI and W₂ cancorrespond to subband PMI.

Alternatively, the precoding vector obtained by linear extension can bedecomposed as:

$v_{k} = {{\underset{\underset{W_{1}}{}}{I}\underset{\underset{W_{2}}{}}{{\frac{1}{\left( {1 + {\alpha }^{2}} \right)^{1/2}}\left\lbrack {W_{i}^{(1)},W_{i}^{(2)},W_{i}^{(3)},W_{i}^{(4)}} \right\rbrack}\begin{bmatrix}1 \\a_{2} \\a_{3} \\a_{4}\end{bmatrix}}} = {W_{1}W_{2}}}$

such that W₁=I.

There are two alternatives for selecting α.

Alternative 1: Fixed α

The optimal value for α can be determined based on system simulations.For example, a value of α=0.8 can be used.

Alternative 2: Variable α

For this alternative, larger codebooks must be considered. For example,the codebook can be expanded by increasing the alphabet for α from thesingle value of 0.8 to a set of values such as αε{-0.8, 0.8}. Ingeneral, if the size of the allowed alphabet for α is K, the size of thecodebook is given by 16·(1+3K), and the number of candidate precodersthat must be evaluated by the UE is 16+3K.

Rank-2 Codebook (First Embodiment)

In one embodiment, the existing rank-2 codebook in Table 2 for four Txantennas is specified in the column for υ=2 layers of Table 2. Thecodebook consists of a total of sixteen 4×2 matrices. For rank-2transmissions, the size of this codebook is expanded from 16 to 48 inthe following manner.

To begin, the 16 rank-2 codebooks from Table 2 are included. Thefollowing three 4×4 permutation matrices can then be defined. The firstof these permutation matrices P₁ is the identity matrix. The secondpermutation matrix P₂ exchanges the second and third columns and isgiven by:

$P_{2} = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & 1\end{bmatrix}.}$

The third permutation matrix P₃ exchanges the second and fourth columnsand is given by

$P_{3} = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 0\end{bmatrix}.}$

W_(i,2) can denote the rank-2 precoding matrix corresponding to thecodebook index i in Table 2. With the above permutation matrices, theRelease-8 rank-2 codebook in Table 2 can be expressed as

${W_{i,2} = {{{W_{i} \cdot {P_{m{(i)}}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 0 \\0 & 0\end{bmatrix}} \cdot \frac{1}{\sqrt{2}}}\mspace{31mu} i} = \left\{ {0,1,\ldots \mspace{14mu},15} \right\}}},$

where the unitary matrix W_(n) is W_(n)=I−2u_(n)u_(n) ^(H)/u_(n)^(H)u_(n) where I is the 4×4 identity matrix and the vector u_(n) isgiven by Table 2, and m (0 is given in Table 4:

i= m(i) 0 3 1 1 2 1 3 1 4 3 5 3 6 2 7 2 8 1 9 3 10 2 11 2 12 1 13 2 14 215 1

The codebook from 16 to 48 can be extended by defining

$W_{i,2} = {W_{{mod}{({i,16})}} \cdot P_{m({{mod}{({i,16})}}} \cdot \begin{bmatrix}1 & 0 \\0 & 1 \\\alpha & 0 \\0 & \alpha\end{bmatrix} \cdot \frac{1}{\sqrt{2\left( {1 + {\alpha }^{2}} \right)}}}$i = {16, 17, …  , 31} and$W_{i,2} = {W_{{mod}{({i,16})}} \cdot P_{m({{mod}{({i,16})}}} \cdot \begin{bmatrix}1 & 0 \\0 & 1 \\0 & \alpha \\\alpha & 0\end{bmatrix} \cdot \frac{1}{\sqrt{2\left( {1 + {\alpha }^{2}} \right)}}}$i = {32, 17, …  , 47}

In the enhanced codebook, the triplet (W_(i′,2), W_(i′+16,2),W_(i′+32,2)) where i′=0, 2, . . . , 15 corresponds to the originalcodebook and its linear extensions (e.g., (W_(0,2), W_(16,2), W_(32,2))is one triplet where W_(16,2) and W_(32,2) are linear extensions ofW_(0,2)).

Similar to the rank-1 case, the UE can first choose the best Release 8precoder within the existing set of 16 rank-2 precoders W_(i,2)=, i={0,1, . . . , 15}, and then can determine if this best Release 8 precoder(with codebook index i) can be improved by linear combinations with theunused column vectors (scaled by α) of W_(i). With this method, the UEmay only need to evaluate a total of 18 rank-2 candidate precoders whichincludes first selecting a precoder from the set of 16 existing Release8 rank-2 precoders W_(i,2)=, i={0, 1, . . . , 15}, and then selectingfrom two linear combination rank-2 precoders that depend on the selectedW_(i,2).

Rank-2 Codebook (Second Embodiment)

In another embodiment, the existing rank-2 codebook for four Tx antennasis specified in the column for υ=2 layers of Table 2. The codebookconsists of a total of sixteen 4×2 matrices. For rank-2 transmissions,the size of the codebook is expanded from 16 to 48 in the followingmanner. Each of the rank 2 codebooks in Table 2 can be represented inthe following manner:

${W_{i,2} = {{{W_{i} \cdot \begin{bmatrix}\beta_{1,1}^{i} & \beta_{1,2}^{i} \\\beta_{2,1}^{i} & \beta_{1,2}^{i} \\\beta_{3,1}^{i} & \beta_{1,2}^{i} \\\beta_{4,1}^{i} & \beta_{1,2}^{i}\end{bmatrix} \cdot \frac{1}{\sqrt{2}}}\mspace{31mu} i} = \left\{ {0,1,\ldots \mspace{14mu},15} \right\}}},$

where W_(i,2) denotes the rank two precoding matrix corresponding tocodebook index i in Table 2, and the vectors β_(•,1) ^(i) and β_(•,2)^(i) also depend on the codebook index i. The unitary matrix W_(n) isW_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n) where I is the 4×4 identitymatrix and the vector u_(n) is given by Table 2. The vectors β_(•,1)^(i) and β_(•,2) ^(i) for all i are defined in the Table 5 below.

TABLE 5 Vectors β_(.,1) ^(i) and β_(.,2) ^(i) for Release 8 codebook i =β_(1,1) ^(i) β_(2,1) ^(i) β_(3,1) ^(i) β_(4,1) ^(i) β_(1,2) ^(i) β_(2,2)^(i) β_(3,2) ^(i) β_(4,2) ^(i) 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 2 1 00 0 0 1 0 0 3 1 0 0 0 0 1 0 0 4 1 0 0 0 0 0 0 1 5 1 0 0 0 0 0 0 1 6 1 00 0 0 0 1 0 7 1 0 0 0 0 0 1 0 8 1 0 0 0 0 1 0 0 9 1 0 0 0 0 0 0 1 10 1 00 0 0 0 1 0 11 1 0 0 0 0 0 1 0 12 1 0 0 0 0 1 0 0 13 1 0 0 0 0 0 1 0 141 0 0 0 0 0 1 0 15 1 0 0 0 0 1 0 0

In order to extend the rank-2 codebook to size 48, the followingadditional pre-coding matrices may be used:

${W_{i,2} = {W_{{mod}{({i,16})}} \cdot \begin{bmatrix}\beta_{1,1}^{i} & \beta_{1,2}^{i} \\\beta_{2,1}^{i} & \beta_{1,2}^{i} \\\beta_{3,1}^{i} & \beta_{1,2}^{i} \\\beta_{4,1}^{i} & \beta_{1,2}^{i}\end{bmatrix} \cdot \frac{1}{\sqrt{2\left( {1 + {\alpha }^{2}} \right)}}}}\mspace{25mu}$ i = {16, 17, …  , 47}

where α=0.8, and β_(•,1) ^(i) and β_(•,2) ^(i) for iε{16, 17, . . . ,47} are defined in Table 6:

TABLE 6 Vectors β_(.,1) ^(i) and β_(.,2) ^(i) for the Enhanced codebooki = β_(1,1) ^(i) β_(2,1) ^(i) β_(3,1) ^(i) β_(4,1) ^(i) β_(1,2) ^(i)β_(2,2) ^(i) β_(3,2) ^(i) β_(4,2) ^(i) 16 1 α 0 0 0 0 α 1 17 1 0 α 0 0 10 α 18 1 0 α 0 0 1 0 α 19 1 0 α 0 0 1 0 α 20 1 α 0 0 0 0 α 1 21 1 α 0 00 0 α 1 22 1 α 0 0 0 0 1 α 23 1 α 0 0 0 0 1 α 24 1 0 α 0 0 1 0 α 25 1 α0 0 0 0 α 1 26 1 α 0 0 0 0 1 α 27 1 α 0 0 0 0 1 α 28 1 0 α 0 0 1 0 α 291 α 0 0 0 0 1 α 30 1 α 0 0 0 0 1 α 31 1 0 α 0 0 1 0 α 32 1 0 α 0 0 α 0 133 1 0 0 α 0 1 α 0 34 1 0 0 α 0 1 α 0 35 1 0 0 α 0 1 α 0 36 1 0 α 0 0 α0 1 37 1 0 α 0 0 α 0 1 38 1 0 0 α 0 α 1 0 39 1 0 0 α 0 α 1 0 40 1 0 0 α0 1 α 0 41 1 0 α 0 0 α 0 1 42 1 0 0 α 0 α 1 0 43 1 0 0 α 0 α 1 0 44 1 00 α 0 1 α 0 45 1 0 0 α 0 α 1 0 46 1 0 0 α 0 α 1 0 47 1 0 0 α 0 1 α 0

In the enhanced codebook, the triplet is, (W_(i′,2), W_(i′+16,2),W_(i′+32,2)) where i′=0, 2, . . . , 15 corresponds to the originalcodebook and its linear extensions (e.g., (W_(0,2), W_(16,2), W_(32,2))is one triplet where W_(16,2) and W_(32,2) are linear extensions ofW_(0,2)).

Similar to the rank-1 case the UE can first choose the best Release 8precoder within the existing set of 16 rank-2 precoders W_(i,2)=, i={0,1, . . . , 15}, and then can determine if this best Release 8 precoder(with codebook index i) can be improved by linear combinations with theunused column vectors (scaled by α) of W_(i). With this method, the UEmay only need to evaluate a total of 18 rank-2 precoders, 16 existingRelease 8 rank-2 precoders=, i={0, 1, . . . , 15}, and two linearcombination rank-2 precoders that depend on the selected W_(i,2).

Simulation Results

An MU-MIMO system simulation with K=10 users, M=4 Tx antennas and N=1receive antennawas performed. A max-rate scheduler that selects up to Musers based on Greedy User Selection (GUS) approach was used.

FIG. 6 shows the mean sum rate for the enhanced codebook for differentvalues of α at SNR=20 dB.

FIG. 7 shows mean sum rate versus SNR for both the Release 8 codebookand the enhanced 4-Tx codebook with α=0.8. In other words, there is nofeedback for α (Approach 2). The codebook enhancement outperformsRelease 8 codebook. At 20 dB SNR, the improvement is about 42.8% or 1.43b/s/Hz.

FIG. 8 shows three embodiments where α is quantized to a finitealphabet. In the first embodiment 7(a), α can take on values from theset {-0.8, 0, 0.8}. In the second embodiment 7(b), α can take on valuesfrom two 4-PSK consetallations with amplitudes 0.6 and 0.9. In additionto 0, there aretherefore 8 values that α can take. In the thirdembodiment 7(c), α can take on values from two 8-PSK constellations withamplitudes r₁ and r₂.

At least a partial representation of the first component matrix (V₁) canbe a first index (i₁). At least a partial representation of the secondcomponent matrix (V₂) can be a second index (i₂). At least a partialrepresentation of α can be a third index (i₃). The first index (i₁) andthe second index (i₂) may be a complete representation of the precodingmatrix (U) when α is selected from a set comprising a pre-determinedvalue (e.g., 0,8) and zero. The second index (i₂) can be used toindicate the 0-valued state for α.

Alternatively, a single joint index (j₁) can be used to represent V₁ andV₂. In one embodiment, the UE 110 is configured with a CSI process forgenerating CSI feedback. The CSI process is associated with thegeneration of one set of CSI which can include PMI, RI, and/or CQI,based on an associated one or more CSI-RS resource(s) (for which the UEassumes non-zero transmission power for the CSI-RS) and one or moreinterference measurement resource. The PMI may correspond to the firstindex (i₁), the second index (i₂), third index (i₃) or the joint index(j₁). The CSI-RS antenna ports corresponding to the CSI-RS resource(s)is associated to one or more antenna elements of an antenna array. TheUE 110 may determine the RI, CQI, the first index (i₁), the second index(i₂) and third index (i₃) based on the CSI-RS received on the CSI-RSantenna ports corresponding to the CSI-RS resource(s) associated withthe CSI process. The PMI and thus the first index (i₁), the second index(i₂) and third index (i₃) are conditioned on the most recent RI. The CQIis conditioned on the most recent PMI. The UE 110 may be configured withperiodic CSI reporting. The UE may be configured with two reportinginstances (first and second reporting instance) each with its ownperiodicities (first and second periodicity) for reporting on a set ofCSI comprising CQI/PMI/RI. The first reporting instance may be in afirst uplink subframe and the second reporting instance may be in asecond uplink subframe. The first uplink subframe and the second uplinksubframe can occur at different times. The first and secondperiodicities may be different.

In one example, the UE may be configured for wideband CQI/wideband PMIperiodic reporting. In one mode of operation, the UE may transmit afirst CSI report including RI and a first PMI, the first PMI being arepresentation of the first index (i₁), on the first reporting instanceswith the first periodicity. The RI and the first PMI may be separatelyencoded (e.g. mapped to different set of bits in a message) or jointlyencoded. In some cases, the first index (i₃) may be sub-sampled (i.e.,only certain specified values or a subset of the possible values areavailable to select from) to fit within the available number of bits forthe first CSI report. The UE 110 may transmit a second CSI reportincluding the wideband CQI and second PMI, the second PMI being arepresentation of the second index (i₂), on the second reportinginstances with the second periodicity. The wideband CQI and the secondPMI may be separately or jointly encoded. Alternatively, the UE 110 maytransmit a second CSI report including the wideband CQI and second PMI(the second PMI being a representation of the second index (i₂)), andthird PMI (the third PMI being a representation of the third index(i₃)), on the second reporting instances with the second periodicity.The wideband CQI, second PMI and the third PMI may be separately orjointly encoded. In some cases, the first codebook index (i₁) and/or thesecond codebook index (i₂) may be sub-sampled (i.e., only certainspecified values or a subset of the possible values are available toselect from) to fit within the available number of bits for the secondCSI report.

In another configured mode of operation, the UE may transmit a first CSIreport including RI and a first PMI, the first PMI being arepresentation of the first index (i₁) and the third index (i₃), on thefirst reporting instances with the first periodicity. The RI and thefirst PMI may be separately encoded (e.g. mapped to different set ofbits in a message) or jointly encoded. In some cases, the first index(i₁) and/or the third index (i₃) may be sub-sampled (i.e., only certainspecified values or a subset of the possible values are available toselect from) to fit within the available number of bits for the firstCSI report. The UE 110 may transmit a second CSI report including thewideband CQI and second PMI, the second PMI being a representation ofthe second index (i₂), on the second reporting instances with the secondperiodicity. The wideband CQI and the second PMI may be separately orjointly encoded. In some cases, the second index (i₂) may be sub-sampled(i.e., only certain specified values or a subset of the possible valuesare available to select from) to fit within the available number of bitsfor the second CSI report.

In another mode of operation, the UE may transmit a first CSI reportincluding RI on the first reporting instances with the firstperiodicity. The UE 110 may transmit a second CSI report including thewideband CQI and PMI, the PMI being a representation of the first index(i₁), the second index (i₂), and the third index (i₃), on the secondreporting instances with the second periodicity. The wideband CQI andthe PMI may be separately or jointly encoded. In some cases, the firstindex (i₁), the second index (i₂), and/or the third index (i₃) may besub-sampled (i.e., only certain specified values or a subset of thepossible values are available to select from) to fit within theavailable number of bits for the second CSI report. In one embodiment,the UE 110 may be signaled an operation mode from a set of modes(including one or more modes described above) by the eNB 120. Thedifferent modes can exploit different feedback rates described andtradeoff the subsampling impacts of the codebook index or indices andprovide mechanisms to minimize the uplink overhead for CSI feedback.

In another example, the UE may be configured for suband CQI/PMI periodicreporting. In one mode of operation, the UE may determine a PrecoderType Indicator (PTI) and transmit a first CSI report including RI andthe PTI on the first reporting instances with the first periodicity. TheRI and the PTI may be separately or jointly encoded. The UE 110 uses thePTI to indicate the contents of the CSI reports on the second reportinginstances with the second periodicity until the next RI+PTI report. Ifthe most recent transmitted PTI is set to ‘0’ (first state) or ‘2’(third state), the UE 110 transmits a second CSI report on a subset ofthe second reporting instances with a third periodicity (e.g., thirdperiodicity=k*second periodicity, k being an integer). If the mostrecent transmitted PTI is set to ‘0’, the second CSI report includes afirst PMI, the first PMI being a representation of the first index (i₁).

If the most recent transmitted PTI is set to ‘2’, the second CSI reportincludes a second PMI, the second PMI being a representation of thethird index (i3). Between every two consecutive first/second PMI reportson the second reporting instances with the second periodicity, the UE110 transmits a third CSI report including a wideband CQI and a thirdPMI assuming transmission on a wideband channel bandwidth, the third PMIbeing a representation of the second index (i2). In case of CSI reportcollision due to the UE configured with multiple carriers (carrieraggregation) or multiple serving cells, the UE transmits a CSI report ofonly one serving cell with the CSI report including only therepresentation of the first index (i1) or representation of the thirdindex (i3) have higher priority than other CSI reports including atleast CQI which are dropped.

If the most recent transmitted PTI is set to ‘1’ (second state), the UE110 transmits the second CSI report on a subset of the second reportinginstances with a fourth periodicity (e.g., fourth periodicity=m*secondperiodicity, m being an integer), the second CSI report including thewideband CQI and the third PMI, the third PMI being a representation ofthe second index (i2) assuming transmission on a wideband channelbandwidth. The fourth periodicity can be different than the thirdperiodicity. Between every two consecutive wideband CQI/wideband thirdPMI reports on the second reporting instances with the secondperiodicity, the UE 110 transmits a fourth CSI report including asubband CQI and a fourth PMI assuming transmission on a subband channelbandwidth, the fourth PMI being a representation of the second index(i2). Thus, with the use of PTI, in scenarios where first index (i1) andthird index (i3) are not changing, subband feedback of the second index(i2) and associated CQI can be achieved which can improve UE throughputperformance.

In an alternate example, if the most recent transmitted PTI is set to‘0’ (first state) the UE 110 transmits a second CSI report on a subsetof the second reporting instances with a third periodicity (e.g., thirdperiodicity=k*second periodicity, k being an integer). The second CSIreport includes a first PMI and a second PMI, the first PMI being arepresentation of the first index (i1), and the second PMI being arepresentation of the third index (i3). Between every two consecutivefirst and second PMI reports on the second reporting instances with thesecond periodicity, the UE 110 transmits a third CSI report including awideband CQI and a third PMI assuming transmission on a widebandchannel, the third PMI being a representation of the second index (i2).The UE 110 behavior if the most recent transmitted PTI is set to ‘1’(second state), is the same as described in the previous mode of theoperation above. In case of CSI report collision due to UE configuredwith multiple carriers (carrier aggregation) or multiple serving cells,the UE transmits a CSI report of only one serving cell with the CSIreport including the representation of the first index (i1) and therepresentation of the third index (i3) have higher priority that otherCSI reports including at least CQI which are dropped.

FIG. 9 is a flowchart illustrating the operation of the UE 110 (FIG. 1)according to an embodiment. At 910, the flowchart begins. At 920, the UE110 receives a pilot signal such as a CSI-RS (described above) orCell-specific Reference Signal (CRS) from the eNB 120 (FIG. 1).

At 930, the UE 110 determines the precoding matrix as a linearcombination of u:=(v₁+αv₂)/√{square root over (1+|α|²)} as noted abovewith respect to Equation 5 and the many example implementationsfollowing it. The UE 110 can also transmit a first CSI report includingat least the representation of at least a portion of the precodingmatrix (U) in an uplink subframe. At 940, the UE 110 transmits therepresentation of at least a portion of the precoding matrix (U) (e.g.,as shown in FIG. 8 and the accompanying description) an uplink subframeover one of a Physical Uplink Shared Channel (PUSCH) and a PhysicalUplink Control Channel (PUCCH). The UE 110 can also transmit CSI, whichcan include one or more of V1, V2 and α. At 950, the flowchart ends.

The methods of this disclosure may be implemented on a programmedprocessor. However, the controllers, flowcharts, and modules may also beimplemented on a general purpose or special purpose computer, aprogrammed microprocessor or microcontroller and peripheral integratedcircuit elements, an integrated circuit, a hardware electronic or logiccircuit such as a discrete element circuit, a programmable logic device,or the like. In general, any device on which resides a finite statemachine capable of implementing the flowcharts shown in the figures maybe used to implement the processor functions of this disclosure.

Although not required, embodiments can be implemented usingcomputer-executable instructions, such as program modules, beingexecuted by an electronic device, such as a general purpose computer.Generally, program modules can include routine programs, objects,components, data structures, and other program modules that performparticular tasks or implement particular abstract data types. Theprogram modules may be software-based and/or may be hardware-based. Forexample, the program modules may be stored on computer readable storagemedia, such as hardware discs, flash drives, optical drives, solid statedrives, CD-ROM media, thumb drives, and other computer readable storagemedia that provide non-transitory storage aside from a transitorypropagating signal. Moreover, embodiments may be practiced in networkcomputing environments with many types of computer systemconfigurations, including personal computers, hand-held devices,multi-processor systems, microprocessor-based or programmable consumerelectronics, network personal computers, minicomputers, mainframecomputers, and other computing environments.

While this disclosure has been described with specific embodimentsthereof, it is evident that many alternatives, modifications, andvariations will be apparent to those skilled in the art. For example,various components of the embodiments may be interchanged, added, orsubstituted in the other embodiments. Also, all of the elements of eachfigure are not necessary for operation of the disclosed embodiments. Forexample, one of ordinary skill in the art of the disclosed embodimentswould be enabled to make and use the teachings of the disclosure bysimply employing the elements of the independent claims. Accordingly,the embodiments of the disclosure as set forth herein are intended to beillustrative, not limiting. Various changes may be made withoutdeparting from the spirit and scope of the disclosure.

In this disclosure, relational terms such as “first,” “second,” and thelike may be used solely to distinguish one entity or action from anotherentity or action without necessarily requiring or implying any actualsuch relationship or order between such entities or actions. The phrase“at least one of” followed by a list is defined to mean at least one of,but not necessarily all of, the elements in the list. The terms“comprises,” “comprising,” or any other variation thereof, are intendedto cover a non-exclusive inclusion, such that a process, method,article, or apparatus that comprises a list of elements does not includeonly those elements but may include other elements not expressly listedor inherent to such process, method, article, or apparatus. An elementproceeded by “a,” “an,” or the like does not, without more constraints,preclude the existence of additional identical elements in the process,method, article, or apparatus that comprises the element. Also, the term“another” is defined as at least a second or more. The terms“including,” “having,” and the like, as used herein, are defined as“comprising.”

We claim:
 1. A method in a wireless terminal comprising: receiving apilot signal from a base station; determining a precoding matrix as alinear combination of two matrices and V₂; based on the received pilotsignal, wherein the two matrices V₁ and V₂ are sub-matrices of a matrixU of a codebook, the linear combination is u:=(V₁+αV₂)/√{square rootover (1+|α|²)} and α is one of a real-valued number and a complex-valuednumber; and transmitting a representation of at least a portion of thedetermined precoding matrix to the base station.
 2. The method of claim1 wherein, V₁ and V₂ are distinct columns of U.
 3. The method of claim1, wherein α is a predetermined value.
 4. The method of claim 1, whereina column of matrix U is a null vector.
 5. The method of claim 1, whereintransmitting the representation of at least a portion of the determinedprecoding matrix comprises transmitting, by the wireless terminal, achannel state information report.
 6. The method of claim 5, wherein thechannel state information report includes one or more of rank indicationand channel quality indication information for one or more spatiallayers, and wherein the channel quality indication for one or morespatial layers is conditioned on the determined precoding matrix.
 7. Themethod of claim 1, wherein transmitting the representation of at least aportion of the determined precoding matrix comprises: transmitting, bythe wireless terminal, a first channel state information reportincluding at least a representation of V₁ in a first uplink subframe,and a second channel state information report including at least arepresentation of V₂ in a second uplink subframe.
 8. The method of claim7, wherein transmitting the representation of at least a portion of thedetermined precoding matrix comprises: transmitting, by the wirelessterminal, a representation of a in one of the first channel stateinformation report or the second channel state information report. 9.The method of claim 7, wherein the first uplink subframe occurs at adifferent time from the second uplink subframe.
 10. The method of claim7, wherein the first channel state information report and the secondchannel state information report are transmitted periodically.
 11. Themethod of claim 11, wherein the first and second channel stateinformation reports are transmitted with different periodicities. 12.The method of claim 1, wherein transmitting the representation of atleast a portion of the determined precoding matrix comprises:transmitting, by the wireless terminal, a representation of a.
 13. Themethod of claim 1, wherein transmitting the representation of at least aportion of the determined precoding matrix comprises: transmitting, bythe wireless terminal, the representation of the precoding matrix overone of a Physical Uplink Shared Channel and a Physical Uplink ControlChannel.
 14. The method of claim 1, wherein the pilot signal is achannel state information reference signal.
 15. The method of claim 14,further comprising receiving a configuration signal indicating one ormore of a number of antenna ports, a periodicity and a subframe offsetapplicable to the channel state information reference signal.
 16. Themethod of claim 1 wherein the pilot signal is a cell-specific referencesignal.
 17. The method of claim 1 wherein U is a 4×4 unitary matrixobtained from Householder reflection, U=I−2rr^(H), where r is a unitvector and r^(H) is the Hermitian-conjugate of r.
 18. The method ofclaim 1 further comprising: determining V₁ that maximizes a first metricbased on the pilot signal; determining V₂ based on V₁ and the pilotsignal.
 19. The method of claim 18 wherein determining V₂ based on V₁and the pilot signal further comprising selecting V₂ from a first setcandidates, the set of candidates being determined by V₁.
 20. A wirelessterminal comprising: a plurality of antennas configured to receive apilot signal from a base station; a controller configured to determine aprecoding matrix as a linear combination of two matrices V₁ and V₂;based on the received pilot signal, wherein the two matrices V₁ and V₂are sub-matrices of a matrix U of a codebook, the linear combination isu:=(V₁+αV₂)√{square root over (1+|α|²)} and α is one of a real-valuednumber and a complex-valued number; and a transceiver configured totransmit a representation of at least a portion of the determinedprecoding matrix to the base station.